Combining rules for intermolecular potential parameters. II. Rules for the Lennard‐Jones (12–6) potential and the Morse potential

Thermodynamics of the van der Waals Dimers of O2, N2 and the Heterodimer (N2)(O2) and Their Presence in Earth's Atmosphere

The dimerization thermodynamics of N2 and O2, the principal components of Earth's atmosphere, have been determined from the respective second virial coefficients of the bound and metastable dimers calculated using the method of Stogryn and Hirschfelder that utilizes the Lennard-Jones (LJ) potential to account for intermolecular interactions. In addition, the thermodynamic properties of the heterodimer (N2)(O2) have been obtained using the same approach, employing combining rules to construct the LJ potential. Thus, Keq, ΔH, and ΔS for the three dimers are reported between 80-120 K. Over this temperature range, the ranking of Keq is (N2)(O2) > (O2)(O2) > (N2)(N2). The same trend is found for the exoethalpicity of dimer formation. For example, at 100 K, the Keq values are, respectively, 0.0406(14), 0.0215(5), and 0.0181(10), and the corresponding ΔH values are -2401(5), -2344(7), and -2279(1) J/mol. The mole fraction composition of the dimers in the atmosphere was calculated for altitudes up to 20 km. These calculations show that in the troposphere and the lower stratosphere (up to 20 km), the three dimers rank fifth to seventh in abundance, between CO2 and Ne. In this region, the average mole fractions of (N2)(N2), (O2)(O2), and (N2)(O2) are calculated to be 3.4(2) × 10-4, 2.80(9) × 10-5, and 1.95(7) × 10-4, respectively.

Accurate and Efficient Estimation of Lennard-Jones Interactions for Coarse-Grained Particles via a Potential Matching Method

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

Selective solvent conditions influence sequence development and supramolecular assembly in step-growth copolymerization

Sequence control in synthetic copolymers remains a tantalizing objective in polymer science due to the influence of sequence on material properties and self-organization. A greater understanding of sequence development throughout the polymerization process will aid the design of simple, generalizable methods to control sequence and tune supramolecular assembly. In previous simulations of solution-based step-growth copolymerizations, we have shown that weak, non-bonding attractions between monomers of the same type can produce a microphase separation among the lengthening nascent oligomers and thereby alter sequence. This work explores the phenomenon further, examining how effective attractive interactions, mediated by a solvent selective for one of the reacting species, impact the development of sequence and the supramolecular assembly in a simple A-B copolymerization. We find that as the effective attractions between monomers increase, an emergent self-organization of the reactants causes a shift in reaction kinetics and sequence development. When the solvent-mediated interactions are selective enough, the simple mixture of A and B monomers oligomerize and self-assemble into structures characteristic of amphiphilic copolymers. The composition and morphology of these structures and the sequences of their chains are sensitive to the relative balance of affinities between the comonomer species. Our results demonstrate the impact of differing A-B monomer-solvent affinities on sequence development in solution-based copolymerizations and are of consequence to the informed design of synthetic methods for sequence controlled amphiphilic copolymers and their aggregates.

Molecular-sized outward-swinging gate: Experiment and theoretical analysis of a locally nonchaotic barrier

We investigate the concept of molecular-sized outward-swinging gate, which allows for entropy decrease in an isolated system. The theoretical analysis, the Monte Carlo simulation, and the direct solution of governing equations all suggest that under the condition of local nonchaoticity, the probability of particle crossing is asymmetric. It is demonstrated by an experiment on a nanoporous membrane one-sidedly surface-grafted with bendable organic chains. Remarkably, through the membrane, gas spontaneously and repeatedly flows from the low-pressure side to the high-pressure side. While this phenomenon seems counterintuitive, it is compatible with the principle of maximum entropy. The locally nonchaotic gate interrupts the probability distribution of the local microstates, and imposes additional constraints on the global microstates, so that entropy reaches a nonequilibrium maximum. Such a mechanism is fundamentally different from Maxwell's demon and Feynman's ratchet, and is consistent with microscopic reversibility. It implies that useful work may be produced in a cycle from a single thermal reservoir. A generalized form of the second law of thermodynamics is proposed.

Kinetic separation of C2H6/C2H4 in a cage-interconnected metal–organic framework: an interaction-screening mechanism

Multi-scale simulations were carried out on a cage-interconnected metal-organic framework (JNU-2), revealing a rarely observed interaction-screening mechanism that corroborates its large C2H6/C2H4 adsorption selectivity.

Global Optimization of the Lennard-Jones Parameters for the Drude Polarizable Force Field

Molecular dynamics (MD) simulations based on atomic models play an important role in the drug-discovery process to screen molecules, estimate binding free energies, and optimize lead compounds in chemical space. Accurate computations of thermodynamic and kinetic properties using MD simulations are highly dependent on the accuracy of the underlying atomic force field. In this context, going beyond the nonpolarizable fixed-charge model by accounting explicitly for induced polarization is highly desirable. The CHARMM polarizable force field based on classical Drude oscillators, in which an auxiliary charged particle is attached via a harmonic spring to its parent nucleus, offers both a computationally convenient and rigorous framework to model explicitly induced electronic polarization in MD simulations. For any molecule of interest, electrostatic partial charges, atomic polarizabilities, and Thole shielding factors, as well as bonded parameters can either be determined from ab initio calculations or ascribed from the knowledge-based library of the CHARMM Generalized force field. While this approach is fairly reliable in general, it is well understood that the overall accuracy of the models with respect to thermodynamic properties such as bulk density, enthalpies, and solvation free energies is particularly sensitive to the nonbonded Lennard-Jones (LJ) parameters. In the present study, we systematically refined the set of LJ parameters for the atom types available in the Drude force field to best match the experimental thermodynamic properties for 416 small druglike organic molecules. To further test the transferability of the optimized parameters, the hydration free energy of 372 molecules was computed. The calculations resulted in a small average error of 0.46 kcal/mol and a Pearson R of 0.9, representing a significant improvement over the additive GAFF force field in our previous study, where an average error of ∼2 kcal/mol was obtained. Such an improvement is consistent with the ability of the polarizable Drude model to more accurately model interactions in different environments. The effort provides a roadmap for the global optimization of force field parameters using experimental data. It is hoped that the present effort will further the application of the Drude polarizable force field in molecular simulations including drug design and discovery.

Breakdown of Universal Scaling for Nanometer-Sized Bubbles in Graphene

We report the formation of nanobubbles on graphene with a radius of the order of 1 nm, using ultralow energy implantation of noble gas ions (He, Ne, Ar) into graphene grown on a Pt(111) surface. We show that the universal scaling of the aspect ratio, which has previously been established for larger bubbles, breaks down when the bubble radius approaches 1 nm, resulting in much larger aspect ratios. Moreover, we observe that the bubble stability and aspect ratio depend on the substrate onto which the graphene is grown (bubbles are stable for Pt but not for Cu) and trapped element. We interpret these dependencies in terms of the atomic compressibility of the noble gas as well as of the adhesion energies between graphene, the substrate, and trapped atoms.

Rayleigh-Brillouin scattering in binary mixtures of disparate-mass constituents: SF_{6}-He,SF_{6}-D_{2}, and SF_{6}-H_{2}

The spectral distribution of light scattered by microscopic thermal fluctuations in binary mixture gases was investigated experimentally and theoretically. Measurements of Rayleigh-Brillouin spectral profiles were performed at a wavelength of 532 nm and at room temperature, for mixtures of SF_{6}-He,SF_{6}-D_{2}, and SF_{6}-H_{2}. In these measurements, the pressure of the gases with heavy molecular mass (SF_{6}) is set at 1 bar, while the pressure of the lighter collision partner was varied. In view of the large polarizability of SF_{6} and the very small polarizabilities of He, H_{2}, and D_{2}, under the chosen pressure conditions these low mass species act as spectators and do not contribute to the light scattering spectrum, while they influence the motion and relaxation of the heavy SF_{6} molecules. A generalized hydrodynamic model was developed that should be applicable for the particular case of molecules with heavy and light disparate masses, as is the case for the heavy SF_{6} molecule, and the lighter collision partners. Based on the kinetic theory of gases, our model replaces the classical Navier-Stokes-Fourier relations with constitutive equations having an exponential memory kernel. The energy exchange between translational and internal modes of motion is included and quantified with a single parameter z that characterizes the ratio between the mean elastic and inelastic molecular collision frequencies. The model is compared with the experimental Rayleigh-Brillouin scattering data, where the value of the parameter z is determined in a least-squares procedure. Where very good agreement is found between experiment and the generalized hydrodynamic model, the computations in the framework of classical hydrodynamics strongly deviate. Only in the hydrodynamic regime both models are shown to converge.

Novel adjustable monolayer carbon nitride membranes for high-performance saline water desalination

In this study, via molecular dynamic simulations, we showed that the latest described graphene-like carbon nitride membranes, such as g-C₄N₃, g-C₆N₆, and g-C₃N₄ single-layers, can be used as high-performance membranes for water desalination. In addition to having inherent nanopores and extraordinary mechanical properties, the carbon nitride membranes have high water permeability and strong ion rejection (IR) capability. The important point about carbon nitride membranes is that the open or closed state of the pores can be changed by applying tensile stress and creating a positive strain on the membrane. The effect of the imposed pressure, the tensile strain, the ion concentration, and the effective pore size of the membranes are reported. It is demonstrated that, with the applied tensile strain of 12%, the g-C₆N₆ membrane is the best purification membrane, with a water permeability of 54.16 l cm^-2 d^-1 MPa^-1 and the IR of 100%. Its water permeability is one order of magnitude greater than other one-atom-thick membranes.

Molecular dynamics study of convective heat transfer mechanism in a nano heat exchanger

With the rapid development of micro/nano electro-mechanical systems, the convective heat transfer at the micro/nanoscale has been widely studied for the thermal management of micro/nano devices. Here we investigate the convective heat transfer mechanism of a nano heat exchanger by the employment of molecular dynamics simulation with a modified thermal pump method. First, the temperature jump and velocity slip are observed at the wall–fluid interfaces of the nano heat exchanger. Moreover, the larger Kapitza resistance in the entrance region weakens the convective heat transfer. Second, the heat transfer performance of the nano heat exchanger can be improved by increasing the surface wettability of the solid walls owing to more fluid atoms being involved in heat transport at the walls when the wall–fluid interaction is enhanced. Meanwhile, the strong surface wettability results in the appearance of the quasi-solid fluid layers, which improves the heat transfer between walls and fluids. Finally, we point out that when the surface wettability of the nano heat exchanger is weak, the heat transfer of the hot fluid side is better than that of the cold fluid side, while the convective heat transfer performances of the cold and hot fluid sides are reversed when the surface wettability is strong. This is because of the feebler temperature jump of the hot fluid side when wall–fluid interaction is small and the greater velocity slip of the cold fluid side for walls with large wall–fluid interaction.

The convective heat transfer mechanism in a nano heat exchanger is investigated using molecular dynamics simulation.

Amino Acid and Oligopeptide Effects on Calcium Carbonate Solutions

Biological organisms display sophisticated control of nucleation and crystallization of minerals. In order to mimic living systems, deciphering the mechanisms by which organic molecules control the formation of mineral phases from solution is a key step. We have used computer simulations to investigate the effects of the amino acids arginine, aspartic acid, and glycine on species that form in solutions of calcium carbonate (CaCO₃) at lower and higher levels of supersaturation. This provides net positive, negative, and neutral additives. In addition, we have prepared simulations containing hexapeptides of the amino acids to consider the effect of additive size on the solution species. We find that additives have limited impact on the formation of extended, liquid-like CaCO₃ networks in supersaturated solutions. Additives control the amount of (bi)carbonate in solution, but more importantly, they are able to stabilize these networks on the time scales of the simulations. This is achieved by coordinating the networks and assembled additive clusters in solutions. The association leads to subtle changes in the coordination of CaCO₃ and reduced mobility of the cations. We find that the number of solute association sites and the size and topology of the additives are more important than their net charge. Our results help to understand why polymer additives are so effective at stabilizing dense liquid CaCO₃ phases.

Combination Rules and Accurate van der Waals Force Field for Gas Uptakes in Porous Materials

Morse function is suggested to be more suitable for studying the gas adsorption in porous frameworks than the Lennard-Jones and exponential-6 forms. However, there have not been some widely used Morse-based van der Waals force fields (vdW FFs) because of complicated parameterization. Combining rules is usually suggested to reduce the parameterization by calculating the unlike-pair parameters from the information of the like pair. A new set of combination rules (DRS) for Morse-based FF has been proposed in our prior work and shown good performance in the simulation of CH₄ adsorption isotherms in covalent organic frameworks. Inspired by our prior work, we developed an accurate van der Waals FF using high-level ab initio calculations with the DRS combination rules. The validation was conducted by comparing the simulated gas uptakes with the experimental values for various known porous materials. The agreement between simulations and experiments is very good, showing the potential application of the FF and the DRS combination rules.

Predicting the phase behavior of hydrogen in NaCl brines by molecular simulation for geological applications

Hydrogen is targeted to have a significant influence on the energy mix in the upcoming years. Its underground injection is an efficient solution for large-scale and long-term storage. Furthermore, natural hydrogen emissions have been proven in several locations of the world, and the potential underground accumulations constitute exciting carbon-free energy sources. In this context, comprehensive models are necessary to better constrain hydrogen behavior in geological formations. In particular, solubility in brines is a key-parameter, as it directly impacts hydrogen reactivity and migration in porous media. In this work, Monte Carlo simulations have been carried out to generate new simulated data of hydrogen solubility in aqueous NaCl solutions in temperature and salinity ranges of interest for geological applications, and for which no experimental data are currently available. For these simulations, molecular models have been selected for hydrogen, water and Na+ and Cl− to reproduce phase properties of pure components and brine densities. To model solvent-solutes and solutes-solutes interactions, it was shown that the Lorentz-Berthelot mixing rules with a constant interaction binary parameter are the most appropriate to reproduce the experimental hydrogen Henry constants in salted water. With this force field, simulation results match measured solubilities with an average deviation of 6%. Additionally, simulation reproduced the expected behaviors of the H2O + H2 + NaCl system, such as the salting-out effect, a minimum hydrogen solubility close to 57 °C, and a decrease of the Henry constant with increasing temperature. The force field was then used in extrapolation to determine hydrogen Henry constants for temperatures up to 300 °C and salinities up to 2 mol/kgH2O. Using the experimental measures and these new simulated data generated by molecular simulation, a binary interaction parameter of the Soreide and Whiston equation of state has been fitted. The obtained model allows fast and reliable phase equilibrium calculations, and it was applied to illustrative cases relevant for hydrogen geological storage or H2 natural emissions.

Aqueous proton-selective conduction across two-dimensional graphyne

The development of direct methanol fuel cells is hindered by the issue of methanol crossover across membranes, despite the remarkable features resulting from the use of liquid fuel. Here we investigate the proton-selective conduction behavior across 2D graphyne in an aqueous environment. The aqueous proton conduction mechanism transitions from bare proton penetration to a mixed vehicular and Grotthuss transportation when the side length of triangular graphyne pores increases to 0.95 nm. A further increase in the side length to 1.2 nm results in the formation of a patterned aqueous/vacuum interphase, enabling protons to be conducted through the water wires via Grotthuss mechanism with low energy barriers. More importantly, it is found that 2D graphyne with the side length of less than 1.45 nm can effectively block methanol crossover, suggesting that 2D graphyne with an appropriate pore size is an ideal material to achieve zero-crossover proton-selective membranes.

Addressing hysteresis and slow equilibration issues in cavity-based calculation of chemical potentials

In this paper, we explore the strengths and weaknesses of a cavity-based method to calculate the excess chemical potential of a large molecular solute in a dense liquid solvent. Use of the cavity alleviates some technical problems associated with the appearance of (integrable) divergences in the integrand during alchemical particle growth. The excess chemical potential calculated using the cavity-based method should be independent of the cavity attributes. However, the performance of the method (equilibration time and the robustness) does depend on the cavity attributes. To illustrate the importance of a suitable choice of the cavity attributes, we calculate the partition coefficient of pyrene in toluene and heptane using a coarse-grained model. We find that a poor choice for the functional form of the cavity may lead to hysteresis between growth and shrinkage of the cavity. Somewhat unexpectedly, we find that, by allowing the cavity to move as a pseudo-particle within the simulation box, the decay time of fluctuations in the integrand of the thermodynamic integration can be reduced by an order of magnitude, thereby increasing the statistical accuracy of the calculation.

Combination Rules for Morse-Based van der Waals Force Fields

In traditional force fields (FFs), van der Waals interactions have been usually described by the Lennard-Jones potentials. Conventional combination rules for the parameters of van der Waals (VDW) cross-termed interactions were developed for the Lennard-Jones based FFs. Here, we report that the Morse potentials were a better function to describe VDW interactions calculated by highly precise quantum mechanics methods. A new set of combination rules was developed for Morse-based FFs, in which VDW interactions were described by Morse potentials. The new set of combination rules has been verified by comparing the second virial coefficients of 11 noble gas mixtures. For all of the mixed binaries considered in this work, the combination rules work very well and are superior to all three other existing sets of combination rules reported in the literature. We further used the Morse-based FF by using the combination rules to simulate the adsorption isotherms of CH₄ at 298 K in four covalent-organic frameworks (COFs). The overall agreement is great, which supports the further applications of this new set of combination rules in more realistic simulation systems.

Kinetic-contact-driven gigantic energy transfer in a two-dimensional Lennard-Jones fluid confined to a rotating pore

A two-dimensional Lennard-Jones system in a circular and rotating container has been studied by means of molecular dynamics technique. A nonequilibrium transition to the rotating stage has been detected in a delayed time since an instant switching of the frame rotation. This transition is attributed to the increase of the density at the wall because of the centrifugal force. At the same time the phase transition occurs, the inner system changes its configuration of the solid-state type into the liquid type. Impact of angular frequency and molecular roughness on the transport properties of the nonrotating and rotating systems is analyzed.

Determination of the Residual Entropy of Simple Mixtures by Monte Carlo Simulation

Extensive Monte Carlo simulations were performed for (neon + krypton) mixtures for temperatures between 200 K and 600 K and pressures up to 1 GPa, using Lennard-Jones potentials to describe the intermolecular interactions. The residual entropies were obtained via Widom's insertion method, as well as via an integration technique. At high pressures, the residual entropy is, to a very good approximation, a linear function of λ_a^-1, which is the reciprocal value of the average Monte Carlo displacement parameter that gives the acceptance ratio a for translational moves. The slope of this linear function varies linearly with the mole fraction and is related to the effective collision diameters of the molecules. As the displacement parameter is available during Monte Carlo simulations of fluids, its linearity with the residual entropy can be used to compute this properties with negligible computational effort at high densities, when particle insertion methods become unreliable.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Water desalination using nano screw pumps with a considerable processing rate

The nano screw pump is used for water desalination while maintaining a considerable, fast water flow.

Adsorption of Quadrupolar, Diatomic Nitrogen onto Graphitized Thermal Carbon Black and in Slit-Shaped Carbon Pores. Effects of Surface Mediation

In this paper, we study the effect of solid surface mediation on the intermolecular potential energy of nitrogen, and its impact on the adsorption of nitrogen on a graphitized carbon black surface and in carbon slit-shaped pores. This effect arises from the lower effective interaction potential energy between two particles close to the surface compared to the potential energy of the same two particles when they are far away from the surface.

A simple equation is proposed to calculate the reduction factor and this is used in the Grand Canonical Monte Carlo (GCMC) simulation of nitrogen adsorption on graphitized thermal carbon black. With this modification, the GCMC simulation results agree extremely well with the experimental data over a wide range of pressure; the simulation results with the original potential energy (i.e. no surface mediation) give rise to a shoulder in the neighbourhood of monolayer coverage and a significant over-prediction of the second and higher layer coverages.

The influence of this surface mediation on the dependence of the pore-filling pressure on the pore width is also studied. It is shown that such surface mediation has a significant effect on the pore-filling pressure. This implies that the use of the local isotherms obtained from the potential model without surface mediation could give rise to a serious error in the determination of the pore-size distribution.

Pore Characterization of Carbonaceous Materials by DFT and GCMC Simulations: A Review

A review is given of the pore characterization of carbonaceous materials, including activated carbon, carbon fibres, carbon nanotubes, etc., using adsorption techniques. Since the pores of carbon media are mostly of molecular dimensions, the appropriate modern tools for the analysis of adsorption isotherms are grand canonical Monte Carlo (GCMC) simulations and density functional theory (DFT). These techniques are presented and applications of such tools in the derivation of pore-size distribution highlighted.

A Comparison of the Elastic Properties of Graphene- and Fullerene-Reinforced Polymer Composites: The Role of Filler Morphology and Size

Nanoscale carbon-based fillers are known to significantly alter the mechanical and electrical properties of polymers even at relatively low loadings. We report results from extensive molecular-dynamics simulations of mechanical testing of model polymer (high-density polyethylene) nanocomposites reinforced by nanocarbon fillers consisting of graphene flakes and fullerenes. By systematically varying filler concentration, morphology, and size, we identify clear trends in composite stiffness with reinforcement. To within statistical error, spherical fullerenes provide a nearly size-independent level of reinforcement. In contrast, two-dimensional graphene flakes induce a strongly size-dependent response: we find that flakes with radii in the 2–4 nm range provide appreciable enhancement in stiffness, which scales linearly with flake radius. Thus, with flakes approaching typical experimental sizes (~0.1–1 μm), we expect graphene fillers to provide substantial reinforcement, which also is much greater than what could be achieved with fullerene fillers. We identify the atomic-scale features responsible for this size- and morphology-dependent response, notably, ordering and densification of polymer chains at the filler–matrix interface, thereby providing insights into avenues for further control and enhancement of the mechanical properties of polymer nanocomposites.

The good, the bad and the user in soft matter simulations

Molecular dynamics (MD) simulations have become popular in materials science, biochemistry, biophysics and several other fields. Improvements in computational resources, in quality of force field parameters and algorithms have yielded significant improvements in performance and reliability. On the other hand, no method of research is error free. In this review, we discuss a few examples of errors and artifacts due to various sources and discuss how to avoid them. Besides bringing attention to artifacts and proper practices in simulations, we also aim to provide the reader with a starting point to explore these issues further. In particular, we hope that the discussion encourages researchers to check software, parameters, protocols and, most importantly, their own practices in order to minimize the possibility of errors. The focus here is on practical issues. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.